Network analyzers are instruments that characterize networks. The characterization result is based on conventions and define how the network will perform under various conditions. In signal integrity applications, the common network parameters in use are s-parameters. S-parameters define port to port relationships in a network when the network is driven by a source whose impedance is set to the reference impedance and all other ports are terminated in that same reference impedance. This convention allows scattering parameters to completely define the behavior of a network under any other driving and termination conditions.
A standard instrument for s-parameter measurement is the vector network analyzer (VNA). This instrument stimulates a network with sinusoidal incident waveforms and measures the reflected sinusoidal waveforms at the network ports, and calculates s-parameters from these measurements. This instrument is most commonly used in the field of microwave analysis.
The VNA needs certain user-defined inputs before it can begin measuring s-parameters. For example it needs the frequency points of interest. Having obtained the user-defined inputs, one needs to calibrate the VNA to eliminate systematic errors in the instrument. If the user-defined inputs change, for example if the user decides to choose different frequency points for s-parameters, then the VNA necessarily needs to be calibrated again. This is an unnecessary time consuming exercise.
There are certain desirable properties of s-parameters that one may expect from certain kinds of networks. For example, one may have the knowledge of whether the network to be analyzed is reciprocal. Frequently the s-parameters measured by the VNA are analyzed in conjunction with other networks using some simulation methods and the user may expect the s-parameters to satisfy some constraints based on the knowledge of the network. During the course of simulation if it is discovered that, the constraints are violated, then the network necessarily needs to be remeasured or the s-parameters need to be processed by an external algorithm to satisfy the known constraints. The external algorithms may not be optimal.
Another instrument used for s-parameter measurement uses techniques called time domain reflectometry (TDR) and time domain transmission (TDT) (Here we will use the commonly used acronym TDR to represent both techniques, the name of the instrument itself, and time domain analysis in general). TDR stimulates a network with an incident step, or pulse and measures reflected waveforms at the network ports. The device used to generate step or step-like waveform is referred to as pulser and a device used to measure step or a step-like waveform is referred to as sampler.
Traditional, well known TDR instruments require as many pulsers and samplers as the number of ports in the device under test (DUT). Hence the cost of such instruments increases greatly with the increase in the number of ports in the DUT.
Since the s-parameters are described in frequency domain, the time domain measurements made by the TDR instruments should be converted into frequency domain methods. There are techniques to compute frequency response of a step-like waveform. For example the algorithm described by Shaarawi and Riad in “Computing the Complete FFT of a Step-like Waveform” IEEE Transactions on Instrumentation and Measurement, Vol IM-35, No. 1, March 1986 the entire contents thereof being incorporated herein by reference, presents such a technique. Such methods result in incorrect results if the measured step-like waveforms differ in delay or amplitude.
What is needed is a method to calculate s-parameters from measurements made with fewer pulsers and samplers. What is also needed is a method that provides measured s-parameters that are robust to changes in step characteristics like the delay or amplitude. What is also needed is a method that does not require repeated calibration if some of the often used user-defined parameters are changed. What is also needed is a method that can satisfy one or more user-defined constraints at the time of measurements.